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Find the nature of the roots of the following quadratic equations:
5x (x – 2) + 6 = 0
Given: 5x (x – 2) + 6 = 0
5x2 – 10x + 6 = 0
Comparing with standard quadratic equation ax2 + bx + c = 0
a = 5, b = – 10, c = 6
Discriminant D = b2 – 4ac
= (– 10)2 – 4.5.6
= 100 – 120 = – 20 < 0
Hence the equation has no real roots.